A magnetically-supported disk-corona model for Changing-Look AGN transitions

Technical Summary: A Magnetically-Supported Disk-Corona Model for Changing-Look AGN Transitions

Problem Statement
Changing-Look Active Galactic Nuclei (CLAGN) exhibit dramatic spectral and luminosity transitions between Type-1 and Type-2 states on timescales of months to a few years. These transitions occur at low Eddington ratios ($\lambda_{\text{Edd}} \approx 10^{-2}$). Standard $\alpha$-disk theory (Shakura & Sunyaev 1973) fails to explain these phenomena simultaneously:

1. Timescale Discrepancy: The viscous timescale at the radii generating optical/UV continuum ($\sim 10^3 R_g$) is $\sim 500$ years for $10^8 M_\odot$ black holes, orders of magnitude longer than observed transitions.
2. Threshold Discrepancy: Standard models predict thermal-viscous instabilities (S-curves) at higher Eddington ratios ($\lambda_{\text{Edd}} \gtrsim 0.1$) or require advection-dominated slim disks to stabilize high-luminosity states, neither of which aligns with the observed low-ratio triggers and the specific nature of the transitions.

Methodology
The authors utilize the diskvert code to solve a closed set of 1D vertical equations for hydrostatic equilibrium, energy balance, radiative transfer, and magnetic flux evolution. The model assumes a steady, axisymmetric disk-corona system supported by gas, radiation, and magnetic pressures.

• Key Physics: The model incorporates magnetic viscosity ($\alpha_B$) where magnetic pressure can dominate the vertical pressure budget. A warm corona ($kT \sim 0.1\text{--}1$ keV, $\tau \sim 10\text{--}30$) arises self-consistently from magnetic heating (via MRI dynamo or magnetic rope dissipation).
• Diagnostics:
  1. Thermal-Viscous S-curves: The authors map steady-state solutions in the $\lambda_{\text{Edd}}$ vs. column density ($\Sigma$) plane to identify the "knee" (critical Eddington ratio, $\lambda_{\text{crit}}$) where the stable upper branch transitions to an unstable middle branch.
  2. Timescales: They calculate the vertically integrated thermal timescale ($t_{\text{th,int}}$) and the front propagation timescale ($t_{\text{fp}}$), defined as $t_{\text{th,int}} \times (R/H)$, where $H/R$ is the disk aspect ratio.
• Parameter Space: A grid of models was computed varying black hole mass ($M_{\text{BH}} = 10^7\text{--}10^9 M_\odot$), radius ($R = 6\text{--}100 R_{\text{Schw}}$), and magnetic viscosity ($\alpha_B = 0.02\text{--}0.59$).
• Observational Confrontation: The model is tested against a sample of five well-characterized CLAGN (Mkn 590, NGC 1566, IRAS 23226−3843, Mkn 1018, NGC 2617), comparing theoretical $\lambda_{\text{crit}}$ and $t_{\text{fp}}$ against empirical transition Eddington ratios and observed event durations.

Key Results

1. Magnetic Stabilization and the S-Curve Knee:

   • In standard, weakly magnetized models ($\alpha_B \leq 0.4$), the S-curve knee occurs at $\lambda_{\text{Edd}} \gtrsim 0.1$, inconsistent with observations.
   • Strongly magnetized configurations ($\alpha_B \approx 0.40\text{--}0.55$) push the S-curve knee down to $\lambda_{\text{Edd}} \approx 0.01\text{--}0.03$. This matches the empirical transition ratios for the sample, including the tightly constrained value for Mkn 590 ($\log \lambda_{\text{Edd}} = -1.68^{+0.14}_{-0.21}$).
   • The model introduces a new stable upper branch of high-luminosity solutions. Unlike standard thin disks, these solutions are radiatively efficient and radiation-pressure supported but stabilized by magnetic pressure rather than advection.

2. Timescale Resolution:

   • The integrated thermal timescale ($t_{\text{th,int}}$) remains in the days-to-weeks range, too fast to explain CL transitions.
   • The front propagation timescale ($t_{\text{fp}}$), amplified by the disk aspect ratio ($R/H$), falls squarely in the months-to-years range for $M_{\text{BH}} = 10^7\text{--}10^9 M_\odot$. This matches the observed durations of the CLAGN sample.

3. Localization of Instability:

   • Both diagnostics (the location of the S-curve knee and the radius where $t_{\text{fp}}$ matches observed durations) converge on the inner accretion flow ($R \approx 10\text{--}30 R_{\text{Schw}}$).
   • The transition is triggered when the Eddington ratio drops below the critical threshold, causing the inner disk to fall off the stable upper branch and propagate a cooling/heating front outward.

4. Mass Independence:

   • The critical Eddington ratio ($\lambda_{\text{crit}}$) at the knee is found to be essentially independent of black hole mass, suggesting a universal trigger condition across the SMBH mass range.

Significance and Claims
The paper claims to provide the first self-consistent model that simultaneously reproduces both the empirical Eddington ratios and the observed durations of CLAGN transitions.

• Unified Framework: The model demonstrates that strong vertical magnetic support ($\alpha_B \approx 0.4\text{--}0.55$) is the physical mechanism that lowers the instability threshold to observed levels while simultaneously extending the transition timescale via front propagation.
• New Limit Cycle: The authors propose a new limit-cycle mechanism where magnetized disks oscillate between a stable, high-luminosity Type-1 state (with a luminous warm corona and soft X-ray excess) and a stable, low-luminosity Type-2 state (truncated disk, suppressed UV, no warm corona). The transition between these states is driven by radiation-pressure instability in the magnetized inner disk.
• Constraining Power: The case of Mkn 590 is highlighted as a stringent test, where the specific transition Eddington ratio is matched only by a highly magnetized disk-corona flow at small radii ($R \approx 6\text{--}20 R_{\text{Schw}}$).

The authors conclude that while their steady-state model successfully sets the trigger conditions and timescales, a future time-dependent calculation explicitly following the limit cycle is the necessary next step.